Place the milk into a medium saucepan and set it over medium-high heat. Bring the milk to a simmer. Stir in the oats and salt, and cook, uncovered, for 5 minutes, stirring occasionally. Remove the saucepan from the heat and cover it to keep warm.
Meanwhile, heat the olive oil in a medium non-stick skillet over medium-high heat. Add the asparagus and cook, flipping occasionally, until the asparagus is starting to brown in a few places but is still crisp, about 2-3 minutes. Remove the asparagus from the skillet and place it on a clean plate.
Reduce the heat to medium and then crack the eggs into the same skillet you just used to cook the asparagus. Cook the eggs until the whites are firm and no longer opaque and the yolks have started to set, about 2-3 minutes. You can remove the eggs from the skillet for sunny-side up eggs, or flip them and cook them on the second side until your desired level of doneness is reached.
To serve, divide the oatmeal between two bowls. Top each bowl with a fried egg and then sprinkle the tops of the eggs with salt, black and red pepper flakes. Add the asparagus, tomatoes and parsley. Serve immediately.